Sequence - GCD(a,b)>1

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Make an algorithm (the quickest way) for a sequence ($a_n$) of natural number defined as follow:$a_1=1$, $a_2=2$, $\ldots$ , $a_n= gcd(a_{n-1},a_n)>1$. We asking about an index of any number for example: 5 -> 10 332 -> 312